In Connecticut, flags that had been lowered during the somber peak of the coronavirus pandemic were raised to full-staff on Wednesday to signal a return to business.

In Kentucky, gift shops creaked open their doors.

And across Alaska, restaurants, bars and gyms, which have been open to small numbers of customers for weeks, were getting ready to rev back up to full capacity. “It will all be open,” Gov. Mike Dunleavy announced, “just like it was prior to the virus.”

The United States has crossed an uneasy threshold with all 50 states beginning to reopen in some way, two months after the coronavirus thrust the country into lockdown. But there are vast variations in how states are deciding to open up, with some forging far ahead of others.

The increasing moves to lift restrictions on businesses — or at least open up outdoor spaces like beaches and state parks — reflect the immense political and societal pressures weighing on the nation’s governors, even as epidemiologists remain cautious and warn of a second wave of cases.

With millions of people out of work and many Americans entering their third month isolated at home, the push to take action rivals what states faced at the beginning of the crisis, when governors were urged to shut down.

“You have 50 different governors doing 50 different things,” said Andrew Noymer, an associate professor of public health at the University of California, Irvine. “There will be states that open too soon or states that are too conservative. It is hard to thread the needle.”

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Kel Rossiter, owner and lead guide of Adventure Spirit, and a customer walking up Cannon Mountain, N.H., on Wednesday. Smaller outdoor group activities were starting to be allowed in the state.Credit...John Tully for The New York Times

But if reopening has become a buzz word among politicians — many states have issued sweeping documents with color-coded plans to “rebound” and “bounce back” — life remains far from normal in most places across America. Even in Georgia, which opened many businesses last month ahead of other states, restaurants are seeing only about 15 percent of normal traffic, according to data published by OpenTable, a restaurant reservation website.

The White House has said that states should have a “downward trajectory” of cases over a 14-day period before reopening, but many states reopened well short of meeting those benchmarks.Some epidemiologists see warning signs of a rebound, especially in the South, and because it can take as long as three weeks for a newly infected person to become sick enough to go to the hospital, the impact of reopening is unlikely to be detectable immediately.

“We really are playing with fire here in a very broad sense," said Charles Courtemanche, an economist at the University of Kentucky. In a recent paper for the journal Health Affairs, he estimated that the number of confirmed cases in the United States, which reached a million at the end of April, would have been closer to 35 million without the restaurant closures and stay-at-home orders that began in mid-March. “Just because it hasn’t been a catastrophe yet in your state, doesn’t mean it doesn’t have the potential to be,” he said.

Ipakoi Grigoriadis was left to navigate the complexities while fielding breakfast orders at her family’s diner, Pop’s Family Restaurant, in Milford, Conn., which reopened to outdoor dining on Wednesday as Connecticut lifted its stay-at-home order and allowed some businesses to reopen.

“It is still a little scary considering we don’t exactly know what this is,” said Ms. Grigoriadis, who said the restaurant was taking a number of precautions. Employees were instructed to wear masks and gloves at all times, she said, and patrons were expected to wear masks while at the restaurant as well — “except when they are eating and drinking.”

Connecticut was among the last states to take the plunge toward reopening, representing the more cautious approach that has defined much of the Northeast. New York, which has seen by far the most cases and deaths in the nation, is proceeding with a regional reopening that excludes hard-hit New York City. In Washington, D.C., a stay-at-home order is in effect until June and the surrounding region remains closed.

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Mystic Aquarium in Connecticut reopened to some on Wednesday and is expected to reopen to the public on Friday.Credit...Christopher Capozziello for The New York Times

Several states on the West Coast and certain Democratic-led states in the Midwest have also moved slowly, taking a regional or step-by-step approach.

By contrast, a number of states in the South opened earlier and more fully. Businesses have been open with social distancing requirements for nearly a month in Georgia, where the number of new cases has remained more or less the same. Mississippi saw its largest single-day increase in reported cases and deaths only after the state began to reopen.

Texas, the nation’s second-largest state, with 29 million residents, had among the shortest stay-at-home orders in the country when it reopened many businesses on May 1, in a move that appealed to the state’s pro-business spirit. But weeks later, officials reported the highest one-day total of new cases, and some fear many businesses will still not survive.

Of the more than 50,000 restaurants in Texas, 12 percent have gone out of business because of the pandemic, said Emily Williams Knight, chief executive of the Texas Restaurant Association. She said she expected that up to 30 percent would “not make it through the crisis.” The state’s restaurant industry has already lost 700,000 jobs, she said, and would most likely lose more.

“I think you see customers now having an emotional impact of driving up and having a restaurant they’ve spent years at simply closed, with a note saying, ‘Thank you for your patronage over the years,’” she said.

While scores of restaurants flounder or even collapse, El Arroyo, a popular Mexican restaurant at the western edge of downtown Austin, found a ticket to survival with a savvy marketing move — the sale of to-go margaritas. The restaurant has since begun serving customers on its patio and will return to indoor dining when Texas allows restaurants to expand to 50 percent capacity for indoor sales from 25 percent, starting Friday.

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A group of people removed their masks to eat lunch outside of Central Market, a Texas grocery chain, this month.Credit...Ilana Panich-Linsman for The New York Times

“We’re full,” said Shane Thompson, the manager. “People are happy to be out and about.”

In Louisville, Ky., a handful of customers browsed through the bourbon, horse-themed jewelry and collectible items that stocked the Kentucky Derby Museum gift shop on Wednesday, when the state lifted restrictions on retail stores.

Frequently Asked Questions and Advice

Updated June 5, 2020

How many people have lost their jobs due to coronavirus in the U.S.?

The unemployment rate fell to 13.3 percent in May, the Labor Department said on June 5, an unexpected improvement in the nation’s job market as hiring rebounded faster than economists expected. Economists had forecast the unemployment rate to increase to as much as 20 percent, after it hit 14.7 percent in April, which was the highest since the government began keeping official statistics after World War II. But the unemployment rate dipped instead, with employers adding 2.5 million jobs, after more than 20 million jobs were lost in April.

Will protests set off a second viral wave of coronavirus?

Mass protests against police brutality that have brought thousands of people onto the streets in cities across America are raising the specter of new coronavirus outbreaks, prompting political leaders, physicians and public health experts to warn that the crowds could cause a surge in cases. While many political leaders affirmed the right of protesters to express themselves, they urged the demonstrators to wear face masks and maintain social distancing, both to protect themselves and to prevent further community spread of the virus. Some infectious disease experts were reassured by the fact that the protests were held outdoors, saying the open air settings could mitigate the risk of transmission.

How do we start exercising again without hurting ourselves after months of lockdown?

Exercise researchers and physicians have some blunt advice for those of us aiming to return to regular exercise now: Start slowly and then rev up your workouts, also slowly. American adults tended to be about 12 percent less active after the stay-at-home mandates began in March than they were in January. But there are steps you can take to ease your way back into regular exercise safely. First, “start at no more than 50 percent of the exercise you were doing before Covid,” says Dr. Monica Rho, the chief of musculoskeletal medicine at the Shirley Ryan AbilityLab in Chicago. Thread in some preparatory squats, too, she advises. “When you haven’t been exercising, you lose muscle mass.” Expect some muscle twinges after these preliminary, post-lockdown sessions, especially a day or two later. But sudden or increasing pain during exercise is a clarion call to stop and return home.

My state is reopening. Is it safe to go out?

States are reopening bit by bit. This means that more public spaces are available for use and more and more businesses are being allowed to open again. The federal government is largely leaving the decision up to states, and some state leaders are leaving the decision up to local authorities. Even if you aren’t being told to stay at home, it’s still a good idea to limit trips outside and your interaction with other people.

What’s the risk of catching coronavirus from a surface?

Touching contaminated objects and then infecting ourselves with the germs is not typically how the virus spreads. But it can happen. A number of studies of flu, rhinovirus, coronavirus and other microbes have shown that respiratory illnesses, including the new coronavirus, can spread by touching contaminated surfaces, particularly in places like day care centers, offices and hospitals. But a long chain of events has to happen for the disease to spread that way. The best way to protect yourself from coronavirus — whether it’s surface transmission or close human contact — is still social distancing, washing your hands, not touching your face and wearing masks.

How can I protect myself while flying?

If air travel is unavoidable, there are some steps you can take to protect yourself. Most important: Wash your hands often, and stop touching your face. If possible, choose a window seat. A study from Emory University found that during flu season, the safest place to sit on a plane is by a window, as people sitting in window seats had less contact with potentially sick people. Disinfect hard surfaces. When you get to your seat and your hands are clean, use disinfecting wipes to clean the hard surfaces at your seat like the head and arm rest, the seatbelt buckle, the remote, screen, seat back pocket and the tray table. If the seat is hard and nonporous or leather or pleather, you can wipe that down, too. (Using wipes on upholstered seats could lead to a wet seat and spreading of germs rather than killing them.)

Should I wear a mask?

The C.D.C. has recommended that all Americans wear cloth masks if they go out in public. This is a shift in federal guidance reflecting new concerns that the coronavirus is being spread by infected people who have no symptoms. Until now, the C.D.C., like the W.H.O., has advised that ordinary people don’t need to wear masks unless they are sick and coughing. Part of the reason was to preserve medical-grade masks for health care workers who desperately need them at a time when they are in continuously short supply. Masks don’t replace hand washing and social distancing.

What should I do if I feel sick?

If you’ve been exposed to the coronavirus or think you have, and have a fever or symptoms like a cough or difficulty breathing, call a doctor. They should give you advice on whether you should be tested, how to get tested, and how to seek medical treatment without potentially infecting or exposing others.

“We really didn’t know what to expect,” said Rachel Collier, a spokeswoman for the museum, which remains closed even as the gift shop opened back up. She said the museum’s revenue had declined by 95 percent during the pandemic, which also forced the Kentucky Derby to be postponed for the first time in 75 years.

Even without the boon of tourism, she said, a small but steady stream of customers drifted through the gift shop on Wednesday, many eager to buy cups engraved with this year’s canceled derby date. “We are pleasantly surprised,” she said.

Researchers expect that reopening the United States could cause thousands of additional deaths, while also saving several million jobs, a balancing act that has swung more toward the economy in recent weeks.

Researchers found that the biggest risk for negative health outcomes was probably not state regulations, but people’s own behavior. If Americans get out of the habit of social distancing — returning to their pre-pandemic behavior by not wearing masks or staying six feet apart — the forecast predicted that deaths could rise by as many as 135,000.

“Everyone wants us to talk about policy, but in fact personal behavior still matters a lot here,” said Kent Smetters, the faculty director at the Penn Wharton Budget Model.

Many are still hesitant. A new poll by The Associated Press-NORC Center for Public Affairs Research found that most Americans were somewhat concerned that lifting restrictions in their area would lead to new infections, and at least half were very or extremely concerned. About six in 10 people were in favor of people remaining in their homes except for essential needs.

Mary Lou Giles, a 73-year-old resident of El Dorado County, Calif., said that she and her husband planned to shelter in place for another several weeks, though businesses in her remote mountain county between Sacramento and Lake Tahoe were allowed to reopen sooner than in other parts of the state.

“I sincerely hope there will not be a surge in Covid cases as a result of what I believe is a premature rush to reopen,” she said. “But I’m not willing to gamble.”